Eddington's The Mathematical Theory of Relativity is arguably the first comprehensive treatise on the mathematical and physical foundations of general relativity. As Prof. Ashtekar explained it in his excellent and informative Foreword "it is comprehensive on three Eddington systematically introduces the tools of differential geometry, explains the (then known) physical consequences of the theory with admirable clarity, and discusses in detail the conceptual underpinning of general relativity." The new publication of Eddington's book is justified not only by its historical value, but also by the fact that it still provides an original and detailed introduction to the deep physical ideas of general relativity and its mathematical formalism, whose "treatment throughout the monograph is clear, sharp and at the same time pedagogical" (from the Foreword).Eddington's enlightening exposition of general relativity "carries interesting lessons for contemporary researchers in gravitational science at all stages of their career. It is therefore fortunate that the Minkowski Institute Press is making this historic monograph easily available once again" (from the Foreword). This book is not a re-publication of the scanned pages of the original publication; the text has been typeset in LaTeX.
Sir Arthur Stanley Eddington, OM, FRS was a British astrophysicist of the early 20th century. The Eddington limit, the natural limit to the luminosity of stars, or the radiation generated by accretion onto a compact object, is named in his honour.
He is famous for his work regarding the Theory of Relativity. Eddington wrote a number of articles which announced and explained Einstein's theory of general relativity to the English-speaking world. World War I severed many lines of scientific communication and new developments in German science were not well known in England. He also conducted an expedition to observe the Solar eclipse of May 29, 1919 that provided one of the earliest confirmations of relativity, and he became known for his popular expositions and interpretations of the theory.
I use this book from time to time to refer to some of the mathematical tools used in relativity. For instance, I recently used it to see how the Reimann curvature tensor is worked out. For anyone reading this book in the last decade, I think the most problematic part is the old notation used; once you get used to it I would say you can have a working reference.
This book is not, however, very explanatory, and you have to read with patience and re-read again, make some exercises on your own etc.. to really understand what is being presented. Its advantage is that it is quite advanced while being kind of old, so it does get you through some of the topics in a language that you should be able to understand (note: if you have some undergrad courses in physics and math, say mid level or advanced).